\documentclass[letterpaper,12pt]{article}
\begin{document}

\begin{equation}
  \hat x[k] = \sum_{n=1}^N e^{-2\pi\imath (n-1)(k-1)} x[n]
\end{equation}

\begin{equation}
  \hat y[k] = \sum_{n=0}^{N-1} e^{-2\pi\imath n(k-1)} y[n]
\end{equation}

\end{document}
